Now, that's a better output than the first one where I just found out that folder /var/mysql didn't exist at all. So I had to mkdir /var/mysql manually to get an error log. And this says the following:

Instructions for initial setup of your database are contained in the directory /usr/local/share/doc/pkg-readmes -- at install time, you missed a message from pkg_add(1) pointing you to this critical documentation.